ALGEBRA II
The Department’s Educational Philosophy
The study of mathematics will enhance the ability of all students to problem
solve and to reason. Through a strong standardized
departmental program that emphasizes problem solving, communicating, reasoning
and proof, making connections, and using
representations, students will develop self-confidence and a positive attitude
towards mathematics.
Our curriculum matches that of the Massachusetts
Mathematics Curriculum Framework, and we are philosophically aligned with the
National Council of Teachers of Mathematics Standards.
Guiding Principles
• Mathematical ideas should be explored in ways that stimulate curiosity, create
enjoyment of mathematics, and develop depth of
understanding.
• Effective mathematics programs focus on problem solving and require teachers
who have a deep knowledge of the discipline.
• Technology is an essential tool in a mathematics education, and all students
should gain facility in using it where advantageous.
• All students should have a high-quality mathematics program.
• Assessment of student learning in mathematics should take many forms to inform
instruction and learning.
• All students should understand the basic structure of mathematics.
• All students should recognize that the techniques of mathematics are
reflections of its theory and structure.
• All students should gain facility in applying mathematical skills and
concepts.
• All students should understand the role of inductive and deductive reasoning
in mathematic and real life situations.
Course Frequency: Full-year course, five times per
week
Credits Offered: Five
Prerequisites: A final grade of at least 70 in both Algebra I and
Geometry
Background to the Curriculum
This course uses the Houghton Mifflin text by Dolciani et al., Algebra 2 and
Trigonometry, 1992 edition. It is the third course in our
accelerated/enriched (AE) program, and the majority of the students enrolled
have taken Algebra I AE and Geometry AE. This
specific text has been used since 1992; this course has used older editions of
this same text since the late 1960s. The text is followed
quite closely; however, the material on Trigonometry and Probability/Statistics
is not covered. The text matches the 2000 edition of
the Massachusetts State Framework recommendations for a second-year Algebra
course and is philosophically aligned with the spirit
of the National Council of Teachers of Mathematics curriculum standards.
Teachers bring in other material where appropriate and
make minor changes as to emphasis on certain topics, after consultation with the
RDL.
Core Topics/Questions/Concepts/Skills
Solving equations and inequalities in one variable
Working with linear relations and functions
Solving systems of linear equations and inequalities
Simplifying polynomial and radical expressions
Analyzing and graphing quadratic relations and functions
The algebra of rational expressions and rational/fractional equations
Exponential and Logarithmic Functions
Theory of Polynomial Equations
Using sequences and series
Course-End Learning Objectives
| Learning objectives | Corresponding state standards, where applicable |
| 1] Solve linear
equations and inequalities, including those with absolute values |
Algebra II.P.8 |
| 2] Graph linear equations and inequalities | Algebra I.P.3 |
| 3] Find the equation of a line given various information | Algebra I.P.5 |
| 4] Find the equations of parallels and perpendiculars | Algebra I.P.6 |
| 5] Solve equations in 2 or 3 variables | Algebra II.P.10 |
| 6] Fit a model to data | Algebra I.D.2 |
| 7] Use appropriate technology to solve problems | Algebra II.P.8 |
| 8] Simplify monomial and polynomial expressions | Algebra I.P.7 |
| 9] Factor polynomials | Algebra II.P.8 |
| 10] Solve quadratic equations by factoring or quadratic formula | Algebra II.P.7 |
| 11] Simplify radical expressions | Algebra II.N.2 |
| 12] Simplify expressions with complex numbers | Algebra II.N.1 |
| 13] Simplify expressions with negative/fractional exponents | Algebra II.N.2 |
| 14] Graph and apply quadratic functions | Algebra I.P.11 |
| 15] Apply the distance and midpoint formulae | Geometry.G.12 |
| 16] Graph the equations of conic sections centered at origin | Precalculus.P.8 |
| 17] Solve systems of simultaneous quadratic equations | Algebra II.P.8 |
| 18] Find the composition and inverse of functions | Algebra II.P.5 |
| 19] Solve variation problems | Algebra II.P.11 |
| 20] Solve rational/fractional equations | Algebra II.P.8 |
| 21] Simplify complex algebraic rational expressions | Algebra II.P.8 |
| 22] Understand and use arithmetic sequences and series | Algebra II.P.2 |
| 23] Understand and use geometric sequences and series | Algebra II.P.2 |
| 24] Solve algebraic word problems | Algebra II.P.8 |
| 25] Draw graphs in 3-space | Geometry G.16 |
| 26] Perform operations with real numbers as exponents | Algebra II.N.2 |
| 27] Find the equations
of the conic sections, given information in the geometric definitions |
Precalculus.P.8 |
| 28] Explain the theory
of equations – Rational Root Theorem and Fundamental Theorem of Algebra |
Algebra II.P.8 |
| 29] Use Synthetic Division and Synthetic Substitution | Algebra II.P.8 |
| 30] Convert between exponential and logarithmic form | Algebra II.P.4 |
| 31] Apply the log definition and the log laws | Algebra II.P.8 |
| 32] Solve Exponential Equations | Algebra II.P.10 |
| 33] Use determinants in solving systems of equations | Algebra II.P.9 |
| 34] Study patterns that are iterative and recursive | Algebra II.P.1 |
| 35] Identify maximum and minimum values of functions | Algebra II.P.6 |
| 36] Distinguish between
polynomial, rational, logarithmic, exponential functions |
Algebra II.P.11 |
Assessment
Students are generally assessed by in-class tests and quizzes, which are
administered regularly throughout a marking period.
Generally, two quizzes are equivalent to a test. The students’ attitude, effort,
and quality of homework preparation will also impact
their term grade to a small degree. Teachers informally assess students every
day by asking pivotal questions, as well as questions
involving mechanics or concepts, and the students’ term grades may be positively
affected to a small degree based on their responses.
A standardized midyear examination and final examination are administered to all
students in this course in order to assess their longterm
retention of the course material.
Technology and Health Learning Objectives Addressed in
This Course
(This section is for faculty and administrative reference; students and parents
may disregard.)
| Course activity: skills &/or topics taught | Standard(s) addressed through this activity |
| 1] Graphing calculators to introduce Quadratic function graphs | |
| 2] Graphing calculators
to aid in the solution of Polynomial Equations |
|
| 3] Graphing calculators
to contrast graphs with horizontal or vertical shifts |
Materials and Resources
Teachers use other texts for supplementary ideas, such as the McDougal Littell
Algebra II text and the Glencoe Algebra II text.
Review materials that match both of the departmental examinations are used by
all teachers of the course. Some teachers may employ
the software package “Algebra Plotter Plus” to have students investigate a
concept at the Mac lab. Teachers may also have students
investigate problems with graphing calculators